Reversibility in the Extended Measurement-based Quantum Computation

When applied on some particular quantum entangled states, measurements are universal for quantum computing. In particular, despite the fondamental probabilistic evolution of quantum measurements, any unitary evolution can be simulated by a measurement-based quantum computer (MBQC). We consider the extended version of the MBQC where each measurement can occur not only in the (X,Y)-plane of the Bloch sphere but also in the (X,Z)- and (Y,Z)-planes. The existence of a gflow in the underlying graph of the computation is a necessary and sufficient condition for a certain kind of determinism. We extend the focused gflow (a gflow in a particular normal form) defined for the (X,Y)-plane to the extended case, and we provide necessary and sufficient conditions for the existence of such normal forms

Flow Ambiguity: A Path Towards Classically Driven Blind Quantum Computation

Blind quantum computation protocols allow a user to delegate a computation to a remote quantum computer in such a way that the privacy of their computation is preserved, even from the device implementing the computation. To date, such protocols are only known for settings involving at least two quantum devices: either a user with some quantum capabilities and a remote quantum server or two or more entangled but noncommunicating servers. In this work, we take the first step towards the construction of a blind quantum computing protocol with a completely classical client and single quantum server. Specifically, we show how a classical client can exploit the ambiguity in the flow of information in measurement-based quantum computing to construct a protocol for hiding critical aspects of a computation delegated to a remote quantum computer. This ambiguity arises due to the fact that, for a fixed graph, there exist multiple choices of the input and output vertex sets that result in deterministic measurement patterns consistent with the same fixed total ordering of vertices. This allows a classical user, computing only measurement angles, to drive a measurement-based computation performed on a remote device while hiding critical aspects of the computation.Comment: (v3) 14 pages, 6 figures. expands introduction and definition of flow, corrects typos to increase readability; contains a new figure to illustrate example run of CDBQC protocol; minor changes to match the published version.(v2) 12 pages, 5 figures. Corrects motivation for quantities used in blindness analysi

Which graph states are useful for quantum information processing?

Graph states are an elegant and powerful quantum resource for measurement based quantum computation (MBQC). They are also used for many quantum protocols (error correction, secret sharing, etc.). The main focus of this paper is to provide a structural characterisation of the graph states that can be used for quantum information processing. The existence of a gflow (generalized flow) is known to be a requirement for open graphs (graph, input set and output set) to perform uniformly and strongly deterministic computations. We weaken the gflow conditions to define two new more general kinds of MBQC: uniform equiprobability and constant probability. These classes can be useful from a cryptographic and information point of view because even though we cannot do a deterministic computation in general we can preserve the information and transfer it perfectly from the inputs to the outputs. We derive simple graph characterisations for these classes and prove that the deterministic and uniform equiprobability classes collapse when the cardinalities of inputs and outputs are the same. We also prove the reversibility of gflow in that case. The new graphical characterisations allow us to go from open graphs to graphs in general and to consider this question: given a graph with no inputs or outputs fixed, which vertices can be chosen as input and output for quantum information processing? We present a characterisation of the sets of possible inputs and ouputs for the equiprobability class, which is also valid for deterministic computations with inputs and ouputs of the same cardinality.Comment: 13 pages, 2 figure

Jurisprudential and Legal Perspectives on the Protection of Rights and Freedoms in the 2021 Basic Statute of the Sultanate of Oman

In this paper, we examine the constitutional protection of economic rights and freedoms in the Basic Statute of the Sultanate of Oman. Through descriptive, analytical, and historical approaches, the study identifies the protection and mechanisms for attaining social justice according to the Basic Statute to achieve Omans 2040 vision. The study concludes that courts must refrain from applying laws that violate the Basic Statute, and that weak guarantees of economic and social rights and freedoms hinder their protection and prevent the achievement of Oman Vision 2040. The study recommends spreading a culture of human rights and education on economic, social, and cultural rights, as well as adhering to international human rights conventions and covenants ratified by Oman

Determinism and Computational Power of Real Measurement-based Quantum Computation

International audienceMeasurement-based quantum computing (MBQC) is a universal model for quantum computation. The combinatorial characterisation of determinism in this model, powered by measurements, and hence, fundamentally probabilistic, is the cornerstone of most of the breakthrough results in this field. The most general known sufficient condition for a deterministic MBQC to be driven is that the underlying graph of the computation has a particular kind of flow called Pauli flow. The necessity of the Pauli flow was an open question. We show that the Pauli flow is necessary for real-MBQC, and not in general providing counterexamples for (complex) MBQC. We explore the consequences of this result for real MBQC and its applications. Real MBQC and more generally real quantum computing is known to be universal for quantum computing. Real MBQC has been used for interactive proofs by McKague. The two-prover case corresponds to real-MBQC on bipartite graphs. While (complex) MBQC on bipartite graphs are universal, the universality of real MBQC on bipartite graphs was an open question. We show that real bipartite MBQC is not universal proving that all measurements of real bipartite MBQC can be parallelised leading to constant depth computations. As a consequence, McKague techniques cannot lead to two-prover interactive proofs

Generalized Flow and Determinism in Measurement-based Quantum Computation

We extend the notion of quantum information flow defined by Danos and Kashefi for the one-way model and present a necessary and sufficient condition for the deterministic computation in this model. The generalized flow also applied in the extended model with measurements in the X-Y, X-Z and Y-Z planes. We apply both measurement calculus and the stabiliser formalism to derive our main theorem which for the first time gives a full characterization of the deterministic computation in the one-way model. We present several examples to show how our result improves over the traditional notion of flow, such as geometries (entanglement graph with input and output) with no flow but having generalized flow and we discuss how they lead to an optimal implementation of the unitaries. More importantly one can also obtain a better quantum computation depth with the generalized flow rather than with flow. We believe our characterization result is particularly essential for the study of the algorithms and complexity in the one-way model.Comment: 16 pages, 10 figure

Optical generation of matter qubit graph states

We present a scheme for rapidly entangling matter qubits in order to create graph states for one-way quantum computing. The qubits can be simple 3-level systems in separate cavities. Coupling involves only local fields and a static (unswitched) linear optics network. Fusion of graph state sections occurs with, in principle, zero probability of damaging the nascent graph state. We avoid the finite thresholds of other schemes by operating on two entangled pairs, so that each generates exactly one photon. We do not require the relatively slow single qubit local flips to be applied during the growth phase: growth of the graph state can then become a purely optical process. The scheme naturally generates graph states with vertices of high degree and so is easily able to construct minimal graph states, with consequent resource savings. The most efficient approach will be to create new graph state edges even as qubits elsewhere are measured, in a `just in time' approach. An error analysis indicates that the scheme is relatively robust against imperfections in the apparatus.Comment: 10 pages in 2 column format, includes 4 figures. Problems with figures resolve

Generalized Flow and Determinism in Measurement-based Quantum Computation

We extend the notion of quantum information flow defined by Danos and Kashefi for the one-way model and present a necessary and sufficient condition for the deterministic computation in this model. The generalized flow also applied in the extended model with measurements in the X-Y, X-Z and Y-Z planes. We apply both measurement calculus and the stabiliser formalism to derive our main theorem which for the first time gives a full characterization of the deterministic computation in the one-way model. We present several examples to show how our result improves over the traditional notion of flow, such as geometries (entanglement graph with input and output) with no flow but having generalized flow and we discuss how they lead to an optimal implementation of the unitaries. More importantly one can also obtain a better quantum computation depth with the generalized flow rather than with flow. We believe our characterization result is particularly essential for the study of the algorithms and complexity in the one-way model.Comment: 16 pages, 10 figure

Dissociation of Motor Task-Induced Cortical Excitability and Pain Perception Changes in Healthy Volunteers

Background: There is evidence that interventions aiming at modulation of the motor cortex activity lead to pain reduction. In order to understand further the role of the motor cortex on pain modulation, we aimed to compare the behavioral (pressure pain threshold) and neurophysiological effects (transcranial magnetic stimulation (TMS) induced cortical excitability) across three different motor tasks. Methodology/Principal Findings Fifteen healthy male subjects were enrolled in this randomized, controlled, blinded, cross-over designed study. Three different tasks were tested including motor learning with and without visual feedback, and simple hand movements. Cortical excitability was assessed using single and paired-pulse TMS measures such as resting motor threshold (RMT), motor-evoked potential (MEP), intracortical facilitation (ICF), short intracortical inhibition (SICI), and cortical silent period (CSP). All tasks showed significant reduction in pain perception represented by an increase in pressure pain threshold compared to the control condition (untrained hand). ANOVA indicated a difference among the three tasks regarding motor cortex excitability change. There was a significant increase in motor cortex excitability (as indexed by MEP increase and CSP shortening) for the simple hand movements. Conclusions/Significance: Although different motor tasks involving motor learning with and without visual feedback and simple hand movements appear to change pain perception similarly, it is likely that the neural mechanisms might not be the same as evidenced by differential effects in motor cortex excitability induced by these tasks. In addition, TMS-indexed motor excitability measures are not likely good markers to index the effects of motor-based tasks on pain perception in healthy subjects as other neural networks besides primary motor cortex might be involved with pain modulation during motor training